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Structural Analysis or Cultural Analysis? Competing Perspectives on the “Standard Pattern”of West African RhythmAuthor(s): KOFI AGAWUSource: Journal of the American Musicological Society, Vol. 59, No. 1 (Spring 2006), pp. 1-46Published by: University of California Press on behalf of the American Musicological SocietyStable URL: http://www.jstor.org/stable/10.1525/jams.2006.59.1.1 .

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Structural Analysis or Cultural Analysis?

Competing Perspectives on the “Standard

Pattern” of West African Rhythm

KOFI AGAWU

Throughout West and Central Africa, as well as parts of the African dias-pora, the rhythmic pattern shown in Example 1 is pervasive. Known

among specialists as the “standard pattern,” it is one of a class of simi-larly functioning patterns referred to as “time lines.” A time line—also calledbell pattern, bell rhythm, guideline, time keeper, topos , and phrasing referent—is a distinctly shaped and often memorable rhythmic figure of modest durationthat is played as an ostinato throughout a given dance composition. In whatis perhaps its best-known manifestation in Southern Ewe dances, the pattern isbeaten on a double-pronged bell as one layer in a polyrhythmic texture com-prising handclaps, rattles, support drums, lead drum(s), and voices. Example 2reproduces the first four bars of Kongo Zabana’s transcription of Slow

Agbekor to show a typical polyrhythmic texture headed (top staff) by a bell(Gakogui ) playing the standard pattern.1

Journal of the American Musicological Society , Vol. 59, Number 1, pp. 1–46, ISSN 0003-0139, electronic ISSN 1547-3848. © 2006 by the American Musicological Society. All rights reserved. Please direct all requests for permission tophotocopy or reproduce article content through the University of California Press’s Rights and Permissions website, at www.ucpress.edu/journals/rights.htm.

I would like to thank Brian Alegant, Dániel Biró, Brian Hyer, Christopher Matthay, MartinScherzinger, and Dmitri Tymoczco for valuable feedback on the ideas presented in this article.

1. Kongo Zabana, African Drum Music , vol. 1, Slow Agbekor (Accra, Ghana: Afram Publica-tions, 1997), 2–3. For a good description of instruments and instrumental functions in theSouthern Ewe drum ensemble, see chapter 4 of James Burns’s “The Beard Cannot Tell Stories tothe Eyelash: Creative Transformation in an Ewe Funeral Dance–Drumming Tradition” (PhDdiss., University of London, School of Oriental and African Studies, 2005). While differences innotational practice are noticeable in the dozens of transcriptions of Agbekor and other Africandrum music made since the 1950s—especially in the use of rests, time signatures, and phrase andtempo markings—the core of the time line appears to be stable.

Ł Ł Ł Ł Ł Ł Ł Example 1 Standard pattern as uninterpreted chain


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2 Journal of the American Musicological Society

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Example 2 Opening four bars of Slow Agbekor as transcribed by Kongo Zabana ( African

Drum Music , vol. 1, Slow Agbekor [Accra, Ghana: Afram Publications, 1997]; used by permission)




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The “Standard Pattern” of West African Rhythm 3

Practically every scholar writing about West African rhythm during the lasthalf century has taken note of time lines. About the stylized war dance, Agbekor, for example, David Locke says that “every act of drumming,singing, and dancing is timed in accordance with the recurring musical phraseplayed on an iron bell.” John Chernoff introduces the instruments of a typicaldrum ensemble by observing that “the bell is like the heartbeat which keepsthings steady.” Kwabena Nketia, who first used the term “time line” in 1963,describes it as “a constant point of reference by which the phrase structure of asong as well as the linear metrical organization of phrases are guided.” And ac-cording to Gerhard Kubik, time-line patterns are “a regulative element inmany kinds of African music,” numbering among the basic “principles of tim-ing.” There is, in short, general consensus that time lines are materially real, widely used, and crucial markers of temporal reference in African ensemblemusic.2

Inevitably, perhaps, the extant literature does not propagate a single, defini-tive perspective on time lines. Disagreements abound, some of them quitefundamental, regarding their nature, musical function, and ultimate signifi-cance. While Kubik, for example, claims that a time-line pattern “representsthe structural core of a musical piece, something like a condensed and ex-tremely concentrated expression of the motional possibilities open to theparticipants (musicians and dancers),”3 Meki Nzewi, without disputing its

2. David Locke, “ Africa: Ewe, Mande, Dagbamba, Shona, BaAka,” in Worlds of Music: An Introduction to the Music of the World’s Peoples , ed. Jeff Todd Titon (London: Prentice Hall,

1996), 86; John Miller Chernoff, African Rhythm and African Sensibility: Aesthetics and Social

Action in African Musical Idioms (Chicago: University of Chicago Press, 1979), 43; J. H.

Kwabena Nketia, African Music in Ghana (Evanston, IL: Northwestern University Press, 1963),

78; Gerhard Kubik, Theory of African Music , vol. 1 (Wilhelmshaven: F. Noetzel, 1994), 44. We

owe the designation “standard pattern” not to A. M. Jones (as is often reported) but to his infor-mant during the 1950s, Desmond Tay, who drew attention to its prevalence in Southern Ewe

dances, including Adzida, Agbadza, Govu, and Atsiagbekor. The term “ African Signature Tune”

appears in Jones’s Studies in African Music , 2 vols. (London: Oxford University Press, 1959),1:210) in reference to the and patterns that stand in antecedent structural re-lation to the standard pattern. John Collins follows Jones’s usage in a recent speculative study,

African Musical Symbolism in Contemporary Perspective: Roots, Rhythms and Relativity (Berlin:

Pro Business, 2004). In 1960 Anthony King, Jones’s colleague at the School of Oriental and African Studies in London, drew attention to a handful of occurrences of the standard pattern in

Yoruba music (King, “Employments of the ‘Standard Pattern’ in Yoruba Music,” African Music 2, no. 3 [1960]: 51–54). Since then, numerous others have used the term. See, for example,David Temperley ’s “Meter and Grouping in African Music: A View from Music Theory,”Ethnomusicology 44 (2000): 80–82, which includes a discussion of “Hemiolas and the ‘StandardPattern’ ”; and Chernoff ’s “The Rhythmic Medium in African Music,” New Literary History 22(1991): 1093–1102. The generic term “time line” (Nketia, African Music in Ghana , 78) hascome to enjoy a more or less stable place in writings about African rhythm. Kubik, however,

prefers the more explicit “time-line pattern.” See, for example, his Angolan Traits in Black Music,Games and Dances of Brazil: A Study of African Cultural Extensions Overseas (Lisbon: Junta de

Investigações Científicas do Ultramar, 1979), 13–22.3. Kubik, Theory of African Music , 45.




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ubiquity, maintains that the time line “is a phrasing referent, not a structuralreferent in African musical thought and ensemble composition.” It mighteven be “purely a statistical equation.” Therefore, attempts “to contrive theo-retical fabrications in order to prove that it is the structural fundamental in African musical creativity and ensemble music composition” are misguided.4

Disagreements betray two broad orientations, one qualitative, the otherquantitative. Qualitatively oriented approaches engage rhythm as a supremely temporal and complex process; they seek its patterns in life, language, andforms of embodiment. Quantitatively oriented analytical approaches, on theother hand, assign numbers to elements in order to establish identity, and thenexploit a series of operations (adding, dividing, and multiplying) to constructpatterns of association among rhythmic elements and groups. Referring

specifically to the figure shown in Example 1 (although her own representa-tion uses the Time Unit Box System rather than staff notation), Ruth Stone writes that it is “played in Africa without reference to the counting or thequantitative means that Western art music might employ. People in the Westfrequently favor a quantitative approach, while the Kpelle [of Liberia]—andmany other peoples in Africa, as well as in places like India—employ the sylla-bles that are spoken in qualitative relationship to one another.”5 Kubik hadearlier drawn attention to mnemonic patterns as forms of oral notation thatconvey timbral, motional and accentual qualities, qualities that do not register

readily in staff notation.6 Other scholars pursuing a qualitative approach havesought to establish the influence of a society ’s modes of time reckoning onthe temporal and rhythmic character of its music,7 given due attention to therhythms of language and declamation,8 drawn attention to the ethical and be-lief systems that constrain attitudes to drumming,9 and proposed a modeloriginating in gesture and terminating in stylized gesture to frame a divergentset of rhythmic behaviors.10

Recent years have seen a surge of interest in quantitative approaches to African rhythm, specifically the mathematical properties of time lines. Already

4. Meki Nzewi, African Music: Theoretical Content and Creative Continuum; The Culture-

Exponent’s Definitions (Olderhausen, Germany: Institut f ür Didaktik populärer Musik, 1997), 33and 35.

5. Ruth M. Stone, Music in West Africa: Experiencing Music, Expressing Culture (New York:

Oxford University Press, 2005), 81.

6. Gerhard Kubik, “Oral Notation of Some West and Central African Time-Line Patterns,”Review of Ethnology 3 (1972): 169–76.

7. Alan P. Merriam, the chapter “ African Musical Rhythm and Concepts of TimeReckoning,” in African Music in Perspective (New York: Garland, 1982): 443–46.

8. Gilbert Rouget, “Tons de la langue en Gun (Dahomey) et tons du tambour,” Revue de musicologie 50 (1964): 3–29. See also Ruth M. Stone, Dried Millet Breaking: Time, Words, and Song in the Woi Epic of the Kpelle (Bloomington: Indiana University Press, 1988).

9. Chernoff, African Rhythm and African Sensibility .

10. Kofi Agawu, African Rhythm: A Northern Ewe Perspective (Cambridge: Cambridge Uni- versity Press, 1995).




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in 1983, Jeff Pressing employed the principles of group theory to explore what he called “cognitive isomorphisms” between pitch and rhythm in various world musical cultures.11 The African material in this fascinating study is

drawn (mainly) from published transcriptions of various West African timelines, each one given a quantitative profile in order to facilitate comparison with European scales, including those associated with American jazz. Thus thepattern in Example 1, rendered durationally as , is held to beequivalent or analogous to the major scale, whose pattern of semitones is also. Pressing’s article was meant to stimulate further research intogeneral cognitive processes and to encourage reflection on ways in which dif-ferent world cultures domesticate analogous patterns of pitch and rhythm forartistic purposes. Jay Rahn, in an article on ostinatos in African music, ex-

plored the numerical properties of 8-, 9-, 12-, 16-, and 24-beat cycles, offereda critique of Pressing’s cognitive isomorphisms, and, in a later study, assem-bled a database of some twenty-fi ve time lines for purposes of comparativeanalysis.12 Kubik ’s remarks about the notable absence of time-line patterns in American Blues include a chart demonstrating “the mathematics of West andCentral African asymmetric time-line patterns” in the form of a pyramidstump.13 Willie Anku’s structural set analyses of two Ghanaian dances, Adowaand Bawa, employ a quantitative approach deriving from set theory in order tolay bare the nature of the lead drummer’s art.14 And perhaps most impor-tantly, mathematician Godfried Toussaint has recently pursued some of thelines of investigation first opened up by Pressing. A study devoted to ten 12/8seven-stroke time lines, for example, retains their interval vectors, dramatizestheir geometrical shapes within a circular representation, and proposes new methods of classification based on rhythmic oddity and offbeatness.15

11. Jeff Pressing, “Cognitive Isomorphisms between Pitch and Rhythm in World Musics: West Africa, the Balkans and Western Tonality,” Studies in Music 17 (1983): 38–61.

12. Jay Rahn, “ Asymmetrical Ostinatos in Sub-Saharan Music: Time, Pitch and Cycles

Reconsidered,” In Theory Only 9, no. 7 (1987): 23–36. Rahn’s time-line database remainsunpublished.

13. Gerhard Kubik, Africa and the Blues (Jackson: University Press of Mississippi, 1999), 54.

14. Willie Anku, Structural Set Analysis of African Music , vol. 1, Adowa (Legon, Ghana:

Soundstage Production, 1992) and Structural Set Analysis of African Music , vol. 2, Bawa (Legon,

Ghana: Soundstage Production, 1993). See also his “Circles and Time: A Theory of StructuralOrganization of Rhythm in African Music,” Music Theory Online 6 (2000), website athttp://www.societymusictheory.org/mto/issues/mto.00.6.1/mto.00.6.1.anku.html (accessed

1 October 2005).

15. Godfried Toussaint, “Classification and Phylogenetic Analysis of African Ternary RhythmTimelines,” in Proceedings of BRIDGES: Mathematical Connections in Art, Music and Science ,University of Granada, Spain, 23–26 July 2003, 25–36. Extended version at http://cgm.cs.mcgill.ca/~godfried/publications/ternary.pdf (accessed 1 October 2005). There is a possible

third category of cognitively oriented studies that would include Bertram Lehmann, “The Syntaxof ‘Clav é’: Perception and Analysis of Meter in Cuban and African Music” (MA thesis, TuftsUniversity, 2002); and Justin London, Hearing in Time: Psychological Aspects of Musical Meter

(New York: Oxford University Press, 2004).




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If Stone is right that African thinking is predominantly qualitative while Western thinking is quantitative, then the studies by Kubik, Pressing, Rahn, Anku, and Toussaint would have to be dismissed immediately as alien to

African modes of musical intellection—etic rather than emic in orientation,perhaps. And indeed, some of the ostensibly objective findings of quantita-tively oriented analysts—such as the isomorphism between the standard pat-tern and the major scale, or the maximal evenness of the standard patternitself, or the high degree of invariance that results from rotation—have so farnot found any corroboration in indigenous African discourse. This is partly because, the existence of counting games notwithstanding, the numericalmode is not the dominant mode in indigenous pedagogy. African discoursesabout music generally stress holism over atomism, integration over separation,

and an across-the-dimensions over a within-a-dimension tendency. To theextent that the numerical mode operates within individual domains, it is hand-icapped in conveying what some feel is the essence of African rhythm.

At the same time, however, several properties revealed in quantitativelyoriented analyses are compelling enough to engender further inquiry. For ex-ample, deep structural parallels between time lines suggest a possible historicalconvergence of today ’s more divergent, often ethnically associated patterns.Could it be, perhaps, that there once was an Ur–time line that over many gen-erations has morphed into the variants we know today? Similarly, might the

fact that the pattern in Example 1 presents a maximal sampling of possiblestarting points explain its historical endurance as an intrinsically mobile andmusically rich resource for many traditional African composers?

These and several related questions about the meaning of African rhythmicpractices need to be approached analytically and with methodological self-awareness, and it is part of my aim in this article to adopt such a stance in illu-minating a single rhythmic pattern, the so-called standard pattern. The choiceof a brief rhythmic pattern should provide a convenient focus for close analy-sis. I seek understanding from both structural and cultural points of view.

Thus, I will describe the pattern in ways that might be acceptable to musictheory, while commenting on the very ecology that sustains each description. At the same time, I will consider the cultural relevance of a number of ostensi-bly objective features that scholars routinely attribute to African rhythm. I endby proposing a simple generative approach as the one that most readily res-onates with African ways of proceeding.

In distributing insights into “structural” and “cultural” categories, I amnot unaware that the terms are fragile. The realm of culture can and does in-corporate structure, while structure itself inevitably has a cultural history. But I

retain the rubrics as broad points of orientation because they seem to me topossess some institutional currency. Structure signifies material attributes me-diated by a precise, mathematical nomenclature, and free of the contingenciesof expressivity. Culture, on the other hand, embraces a broader set of expres-sive attributes that are not necessarily or specifically musical. Structure ac-




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knowledges a degree of autonomy while culture insists on context. The aimhere is not to elevate one form of analysis over another but to foster dialogueand debate between two nominally distinct modes of thinking. If the condi-

tions of possibility for developing a cross-cultural analysis of African rhythmare in any way enhanced by what follows, my aim will have been achieved.16

Narrating the Character of the Standard Pattern

As expressed in Example 1, the standard pattern is a set of attack points (oronsets) and durations (or intervals)—events, in short. In a dance like Agbadza,the pattern might be heard upwards of seven thousand times in the course of a

single four-hour performance. Phenomenally, then, the sound of the standardpattern is very present to all performers, including dancers. It should be em-phasized that the pattern is repeated literally; it does not admit variations at theconceptual or intentional level. This says nothing about the way it is actually perceived, however, especially because perception is shaped by the range of ac-tivity within a fuller rhythmic texture. I only wish to register the intention thatgoverns the production of sound. This unchanging constraint is one reason why some scholars have likened the time-line function to that of a metro-nome.17 The analogy is not entirely felicitous, however, because a metronome

marks tempo, not rhythm. Whereas a metronone notionally marks time ratherthan carves time, a time line uses a carved rhythmic pattern to mark time.

16. A few of the limitations of what is attempted here need to be aired in order to avoid mis-

understanding. First, I have persisted in using the terms “ African” and “ Western” not because Ifail to recognize the reach and complexity of both geocultural spaces but because the terms seem

to me to retain some semiotic potency in the academy. Second, to readers who are bothered by

my use of “ Africa” instead of specific ethnic and subethnic designations (which, in any case, are

products of colonial occupation), it should be said that the authority for any generalization ismore than a matter of statistics; it is a matter of symbolic capital as well. Readers who find comfortin ethnographic specificity are, of course, free to substitute “Southern Ewe” for “ Africa” in whatfollows, but if generalizing is understood as an expression of desire rather as an act of conventional

reportage, then the selective use of “ African” or “ Western” will, I hope, be seen to be strategic.Third, concerning the ruling dichotomy of this article, it is possible to hear a resonance between

culture/structure and other binaries, including emic/etic, hermeneutics/analysis, music as social

fact/music as formal system, extramusical/musical, and insider/outsider. Their fragility notwith-

standing, such oppositions have proved indispensable to many acts of interpretation; the present

context is no exception. Fourth, mindful of the venue in which this article appears, I have taken

the liberty to recapitulate some conventional wisdom about West African ensemble music for

those who do not normally work with African materials. Ethnomusicologists seeking newethnographic data are advised to look elsewhere; I aim, rather, at readers with an interest in

the emerging critical discourse surrounding African music and its ramifications for cross-culturalinterpretation.

17. Nketia African Music in Ghana , 87; idem, The Music of Africa (New York: Norton,

1974), 131.




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If, for the sake of easy identification, we number each attack point of thestandard pattern using integers (Ex. 3), we note immediately that there areseven events (or “elements,” “objects,” “onsets,” “attack points”);18 they manifest only two kinds of duration, long (quarter note) and short (eighthnote). Events 1, 2, 4, 5, and 6 comprise the larger class of longs (fi ve items), while 3 and 7 make up the class of shorts (two items). One feature of the stan-dard pattern, then, is its use of the structural as well as logical minimum of contrasting durational values (a long and a short). This minimality plays a partin establishing the pattern’s foundational character.

How might we narrate the character of the standard pattern? An attempt toconstruct a narrative that conveys the tendencies of this particular sequence of durations lays bare some of its expressive potential while also drawing atten-tion to other structural properties. According to one narrative, shorter dura-tions interrupt sequences of longer durations. That is, an eighth note firstinterrupts a sequence of two quarter notes; then another eighth note inter-

rupts a sequence of not two but three quarter notes. (I use “interrupt” ratherthan “follow ” to register the active nature of the progression and also to ac-knowledge a slew of psychological operators that come into play as we listen

18. What one calls these things betrays a far from negligible conceptual investment. The

terms “element” and “object,” for example, codify substance or material, “attack point” and “on-set” project a temporal awareness based on a moment of inception, while “event” signals a hap-pening within the context of other happenings. Two (among several) authors who grapple with

terminology while proposing their own theories of rhythm are Simha Arom, African Polyphony

and Polyrhythm: Musical Structure and Methodology , trans. Martin Thom, Barbara Tuckett, andRaymond Boyd (Cambridge: Cambridge University Press, 1991; orig. pub. 1985), and

Christopher F. Hasty, Meter as Rhythm (New York: Oxford University Press, 1997). Needless to

say, there is no agreed-upon set of terms for the analysis of African rhythm. For a necessary but by

now dated account, see Robert Kauffman, “ African Rhythm: A Reassessment,” Ethnomusicology 24 (1980): 393–415.

Ł Ł Ł Ł Ł Ł Ł 1 2 3 4 5 6 7

Ł Ł Ł Ł Ł Ł Ł 2 + 2

5

+ 1 +

+

2 + 2

7

+ 2 + 1

Example 3 Standard pattern as event sequence

Example 4 Standard pattern as additive structure




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to a rhythmic pattern such as this.) In this understanding the process emerg-ing as 1–2 event sequence is disrupted by 3, resumed and amplified as 4–5–6before being interrupted again by 7. The process may be understood as an

emergent one: something is waiting to happen—or to be disclosed—but isnot being allowed to play itself out properly. This hermeneutic reading intro-duces an element of tension—a foundational tension we might say — whereby the standard pattern, unlike some other time lines, never achieves internal res-olution, but is permanently marked by a promise, an extensive anacrusis. Suchbuilt-in dynamism may well constitute one source of the pattern’s attractionfor African musicians. In effect, it simultaneously enshrines a circularity sug-gestive of stasis as well as a mobility pointing to a future, qualities that make itespecially appropriate for dance.

A second, implicit narrative reinforces the same emergent property. According to this, the standard pattern may be thought of as a repeating struc-ture with an interposed element. That is, the sequences 1–2–3 and 5–6–7, which occupy the beginning and end of the pattern, are identical, and are sep-arated by 4. Event 4 is thus the center, fulcrum, or point of symmetry. Al-though this description is technically correct, it has little or no culturalcorroboration. One reason for this is that the sum of durations of both units—1–2–3 and 5–6–7—is 5, a number that is implausible as an archetypal rhyth-mic or metric unit in African culture, the more common units being 2 or 3

and their multiples.19 Another is that the interposing of event 4 would imply amode of rhythmic organization in which processes of addition and, by impli-cation, deletion are recognized as legitimate structural processes. As we willsee, however, additive processes are dif ficult to support from an African con-ceptual point of view.

A third narrative hinges on the role of event 3. Since the standard pattern ismeaningful only as a repeated pattern, we might say that event 3, the firstshort in the pattern, introduces a kink, the effect of which is to destabilize thepattern, introduce an element of syncopation. (Event 3 does not accomplish

the work of destabilizing by itself; it is the return to a long at 4 that shows 3 upas a dissenting element, and this suspicion is confirmed as 5 and 6 maintain thesequence of longs.) This confers a quality of extended anacrusis on the4–5–6–7 event sequence. Discharge takes place at the repeat of the pattern. Inthis understanding, once event 3 destabilizes the stability emerging in the 1–2sequence, the consequent instability is not countered until we reattain event 1

19. A. M. Jones put it directly: “The 8, 12, 16 rule is a pretty safe guide and unless the tran-scriber’s notation adds up to one of these numbers he can normally assume that he has madea mistake” (“On Transcribing African Music,” African Music 2, no. 1 [1958]: 14). Anku, in“Circles and Time” (paras. 9–10), makes a similar point in identifying three basic kinds of setin African music: a 12-time point set (with an eighth-note referent), a 16-time point set (with a

sixteenth-note referent), and a cross-set (combining elements of the 12 and 16 sets). Neither

Jones nor Anku recognizes fi ve- or seven-element sets.




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the qualities sensed intuitively and conveyed affectively by African musicians. We are dealing, therefore, with different economies of expression. Neithereconomy is intrinsically superior; they are merely different. But to take refuge

in difference is to overlook aspects of the history, ethics, and politics of knowl-edge construction. It is to downplay the fact that quantification, held as anatural or even universal process in the metropolis, has been brought to bearon analyses of African rhythm with apparently no need for further justification.But quantitative thinking as an institutional practice is a contingent develop-ment, not a necessary or inevitable one. It is propped up by a larger capitalistand political economy, and in the specific case of applications to African music,by an imperial history.24 Imagine, if you will, a new world order in which African approaches to rhythm pedagogy predominated in the American acad-

emy. Patterns would be taught holistically rather than atomistically; theoretical work would privilege gestalten and larger rhythmic units over pulses akinto the movement of millipedes’ feet; and no one would be granted a musicdegree who could not dance!

The question remains, however, for those committed to cross-cultural un-derstanding who do not choose to overlook the politics of ordering knowl-edge: If the original culture-bearers are oblivious to our way of assigningproperties to their rhythmic patterns, are we justified in insisting on the valid-ity of our way? One answer might be that our way is valid because we know it

to be so within our intellectual economy; theirs may be valid too, but not nec-essarily to us. Another answer might be that our way translates their way into amore precise analytic language. Our intellectual economy is stronger becausediscourse about music is cultivated within institutions, not gathered informally from sporadic utterances made at the site of performance. But several follow-up questions arise: Given that they have a way that is knowable by us, what isour ethical responsibility towards that way? Do we make an honest effort tolearn to do things their way, or do we maintain the a priori superiority of our way? In short, if the standard pattern can be produced and analyzed from an

additive conception, and if this mode of production and analysis comes moreeasily to a (Western) individual, why should s/he bother with a manifestly dif-ferent, perhaps more challenging mode of (African) learning?

These are hardly new questions for music scholars; nor do they admit of straightforward answers. Theorists countering the charge of anachronism inanalysis, ethnomusicologists seeking to mediate between insider and outsiderperspectives, and historical musicologists attempting to reconcile the impera-tives of modern thinking with a reconstructed past thinking—all have had toconfront the central questions of appropriate knowledge and power differen-

24. Alan Bishop, “ Western Mathematics: The Secret Weapon of Cultural Imperialism,” Race and Class 32, no. 2 (1990): 51–65.




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tials in intellectual discourse.25 The most honest conclusion may not be theliberal position that we are engaged in some kind of dialogue with historicalothers or geographically distant subjects. Why not admit that whatever we do,

we are obliged to win in the end? If the idea of dialogue provides the front forsuch “ winning,” then so be it. To lose would be to lose ourselves—an entirely unacceptable outcome, many would privately admit, even while publicizing afake egalitarianism. “Our ultimate concern,” writes ethnomusicologistKenneth Gourlay, “is with ourselves and our own culture. . . . At bottom weare in it to save our souls or at least, to find them.”26

Rotational Possibilities

Perhaps the most interesting properties of the standard pattern stem from itsrotational possibilities. Already in 1959 A. M. Jones had noticed that different African communities phrased and accentuated versions of the pattern differ-ently. Anticipating objection to his method of derivation, he landed upon therotational (as distinct from permutational) possibilities of the pattern:

At whatever point in this [] formula you choose to start, if you repeat your pattern, this sequence will appear. Were the Africans to change the orderof the long and short notes, then the basic pattern would be upset. For exam-ple, the sequence [] makes an entirely different basic rhythm and at

whatever point you start in it, you will never, by repetition, produce the familiar[] form. It is this particular sequence of short and long basic units

which is so clearly a typological feature of African music generally.27

The idea that the pattern might be begun at different points and still retaincertain essential features has proved attractive to later scholars. Although athorough, interethnic study of this principle remains to be undertaken, re-search by Pressing and Toussaint suggests that we might gain further insight

into the aesthetic choices of different African communities by exploring fur-ther the principle of rotation.28

25. For one among several fruitful discussions, see chap. 9 (“The Politics of Reception:Tailoring the Present as Fulfilment of a Desired Past”) of Leo Treitler’s With Voice and Pen: Coming to Know Medieval Song and How It Was Made (New York: Oxford University Press,

2003).

26. Kenneth Gourlay, “Towards a Humanizing Ethnomusicology,” Ethnomusicology 26(1982): 411–12.

27. Jones, Studies in African Music , 1:213

28. There are other ways of describing the procedure here referred to as rotation. One may speak of modes by analogy with scales. Just as the Dorian and Phrygian modes use an identical

collection of pitches but with different centers, so the order of the elements in the standard

pattern can be disposed with different starting points. See, among other writings, Pressing’s“Cognitive Isomorphisms” for further discussion of rotations as modes.




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A simple rotation of the seven events that constitute the standard pattern yields the following orderings. (Each durational pattern is then written twiceto reveal the embedding of the initial rotation 0 [in boldface and underlined].)

Rotation 0 Rotation 1 Rotation 2 Rotation 3 Rotation 4 Rotation 5 Rotation 6

Immediately noticeable is the high degree of invariance among rotational

forms—a consequence of the pattern’s maximal evenness. Rotations 0 and 4are identical except for the reversal in the order of elements 6 and 7. Rotations1 and 5 switch their elements 5 and 6, rotations 2 and 6 their elements 4 and5, rotations 3 and 0 their elements 3 and 4, rotations 4 and 1 their elements2 and 3, rotations 5 and 2 their elements 1 and 2, and rotations 6 and 3 theirelements 7 and 1. Rotation, in short, preserves the essence of the pattern.(This says nothing about the cognitive veracity of rotation as such.)

From another point of view, the procedure of rotation reveals that pairsof patterns are related by exchanging their “halves.” (Since each pattern has

seven elements, and since the exchange we are proposing embraces wholeelements, a “half ” should be understood as a succession of 3 or 4 contiguouselements. For these purposes, therefore, sets containing 3 or 4 elements areheld to be equivalent.) Thus, rotation 0, whose “halves” are and respectively, is closely related to rotation 3, whose “halves” are and . In effect the two forms exchange their halves while pre-serving the order within each half. This property obtains for six other pairs: ro-tations 1 and 4, 2 and 5, 3 and 6, 4 and 0, 5 and 1, and 6 and 2. Gesturally,the property is perhaps akin to the kind of hexachordal exchange that pro-

duces aggregates between combinatorial sets, although the preservation oforder in the case of the standard pattern might dissuade us from pressing thatanalogy too far. One might also liken the property to the authentic/plagalpairing of modes in the modal tradition. Rotation, in short, yields a high de-gree of economy within the standard pattern and its derived forms.

What might be the cultural significance of rotation? Jones identified thetwo basic forms of the standard pattern as and . (The lattermay be obtained by rotating the former twice, although Jones spoke of an “in- verted pattern” and different starting points.) He found versions of the former

among the Bemba, Ewe, and Lala, and versions of the latter among the Yoruba, Ewe, Ila, and Tonga. Given their equivalence, he concluded that they are one and the same pattern, a pattern that is “ very deep down in the Africanmusical mind.” He recognized that it is possible to use the “unadulterated ba-sic pattern” or some variant of it.29

29. Jones, Studies in African Music , 1:212.




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Following Jones, Anku has argued that individual African communitiespossess sets of norms of perception. These norms dictate, for example, that an Anlo-Ewe hears the regulative beat of the standard pattern beginning on ele-

ment 1 while a Yoruba hears it beginning on element 4. The Ewe and Yorubapatterns “are derived from the same rhythmic concept. On a deeper level, they are merely perceived with different start points as well as different beat percep-tions.”30 Anku does not provide extensive ethnographic data to support hisassertion, nor does he cite evidence from reception history. Nevertheless, theidea that norms of perception exist within African communities, and that they may differ from community to community, is entirely plausible. In the specificcase of the standard pattern, the prospect of different perceptions of the posi-tion of a regulative beat suggests a collective conceptual investment in rota-

tional equivalence. Subsurface equivalence and surface difference, in turn,indicate a possible common origin for all time lines.31

Does rotation register in African systems of musical thought? Although adefinitive answer is not possible on the basis of the current state of knowledge,none of the published lexicons representing talk about music in indigenouslanguages, or ethnographies shaped by African-language expression, includes aterm for “rotation” as a structuring principle. These include the Kpelle, Igbo, Akan, Vai, Tiv, Dan, and Hausa in West Africa and the Ankole in East Africa.32

These vocabularies tend to privilege affective response, musical genres, instru-

ments and—most importantly for our purposes—terms that convey actions inperformance, not the kinds of technical vocabulary associated with music the-ory ’s structural properties. This is not to say that structural procedures cannotbe teased out of indigenous taxonomies (Arom’s claim that “ African tax-onomies, while adequate from a social and/or religious perspective, throw nolight whatsoever on the systematic structure of the musical techniques em-ployed”33 is surely an overstatement); it is only to concede that the immediateconcerns thematized in the discourse of musicians revolve around the dynam-ics of performance. The absence of terms that support the idea of rotation is

30. Anku, Structural Set Analysis , vol. 1, Adowa , 8.

31. For more on rotation, see Toussaint’s discussion of “rhythm wheels” in “Classificationand Phylogenetic Analysis of African Ternary Rhythm Timelines,” 11–13.

32. See Ruth M. Stone, Let the Inside Be Sweet: The Interpretation of Music Event among the

Kpelle of Liberia (Bloomington: Indiana University Press, 1982); Meki Nzewi, Musical Practice

and Creativity: An African Traditional Perspective (Bayreuth: IWALEWA-Haus, University of

Bayreuth, 1991); J. H. Kwabena Nketia, Akanfo Nnwom Bi [Akan Songs] (London: Oxford

University Press, 1949); Lester P. Monts, An Annotated Glossary of Vai Musical Language and Its

Social Contexts (Paris: Selaf, 1990); Charles Keil, Tiv Song: The Sociology of Art in a Classless Society (Chicago: University of Chicago Press, 1979); Hugo Zemp, Musique Dan: La musique dans la

pensée et la vie sociale d’une société africaine (The Hague: Mouton, 1971); David Ames and

Anthony King, Glossary of Hausa Music and Its Social Contexts (Evanston, IL: Northwestern

University Press, 1971); and Paul van Thiel, Multi-Tribal Music of Ankole: An Ethnomusicological

Study including a Glossary of Musical Terms (Tervuren, Belgium: Musée Royal de l’ AfriqueCentrale, 1977).

33. Arom, African Polyphony and Polyrhythm , 215.




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34. This point is developed as part of an argument against constructions of difference in the

discourse of Africanist ethnomusicology (see my Representing African Music , chap. 7). Veit

Erlmann counters my contestation of difference in “Resisting Sameness: À propos Kofi Agawu’s‘Representing African Music,’ ” Music Theory Spectrum 26 (2004): 291–304.

35. Pressing, “Cognitive Isomorphisms.”

noteworthy; perhaps rotation is simply an extra-African explanatory principle—an imposition from without.

Some readers may object to the method emerging here, namely: subject

Western theoretical terms to an African test and determine their validity onthis basis. They might argue that whether or not rotation registers in Africandiscourse is beside the point; the fact that our metalanguage shows the stan-dard pattern in different rotations used by different ethnic groups is significantin itself. Perhaps—the argument continues, albeit speculatively — African musi-cians may in time come to embrace the term when they see that it codifies what they have been doing for generations. Such an objection should not bedismissed because, as I have argued elsewhere, it is not what Africans say —ordo not say —at a particular historical moment that ultimately matters; rather, itis what is sayable by them— what can be learned to be said—in the moment in which their worlds come into contact with other worlds, when their horizonsfuse with others’ horizons.34

The emergence of this newer, postcolonial vocabulary should cause us totemper the lines we use to distinguish Western reality from African reality. Butto place the accent on the hypothetical, on what might be, is to obscure whatexists. If African musicians have a perfectly coherent way of describing perfor-mance actions that produce specific structures, why not embrace their nomen-clature and modus operandi rather than insist on the validity of our way?

Skepticism about the relevance of “rotation” and other such terms is thereforenot only not inappropriate, but potentially illuminating of the naming prac-tices and critical priorities displayed in indigenous African thinking.

Pitch-Rhythm Isomorphism

Fascination with the standard pattern also comes from the pursuit of analogi-cal structuring. By crossing parametric domains, one notices immediately that

the “ Western” diatonic scale’s intervallic sequence (measured insemitones) and the durational sequence of the African standard pattern (measured in eighth notes) are identical. This equivalence allowsus to transpose any number of formal properties associated with the much-researched diatonic scale (including asymmetry, maximal evenness, and gener-ation by fifths) into the temporal/rhythmic realm. Jeff Pressing providedthe most compelling demonstration of this kind of parallelism in a study of “cognitive isomorphisms” in selected Western and non-Western (including

African) repertoires.35




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The idea that the standard pattern, this most used of African rhythmic pat-terns, finds a ready equivalent in the diatonic major scale, that most used of Western scales, is at the very least sociologically intriguing, and it may rein-

force stereotypical attributions of rhythmic genius to African peoples and pitchgenius to Europeans. But the nature of this analogy needs to be interrogated.Scale systems and rhythmic systems are based on different generative princi-ples, so their processes may not be compared facilely by, for example, equating“intervals” across two separate domains. Moreover, actual musical manifesta-tion would discourage us from pressing the analogy too far: whereas thestandard pattern is a fixed ostinato heard from the beginning to the end of adance composition, the diatonic scale is rarely employed as an ordered intervallic pattern from beginning to end. Pressing himself meant the analogy —not homology —to be suggestive. He surveyed the seven-stroke, 12-set timelines and found their equivalence in the seven modes (ionian, dorian, phry-gian, lydian, mixolydian, aeolian, and two forms of locrian). Special generativepowers accrue to the diatonic major scale and its complement, the pentatonicscale, just as the fi ve-stroke, 12-set pattern described long ago by Jones standsbehind the seven-stroke standard pattern. Pressing speculates on why theseproperties are common to different world cultures, and concludes that they appear to respond to certain cognitive constraints that are expressed in differ-ent material forms.

As before, we must ask whether there is any cultural support for the idea of pitch-rhythm isomorphism. We have already noted that the quantitative orien-tation that facilitates interdimensional—not intersemiotic—comparison is notcharacteristic of African musical discourse. It seems unlikely, therefore, that African musicians would recognize an isomorphism between pitch andrhythm if they saw one. But Pressing’s framing of the insight shares with African thought systems an entangled, potentially holistic approach to build-ing relationships in music. Although the notion of “pure rhythm” seems tohave some currency in Western thought,36 there is nothing like pure rhythm

from an African point of view; rather, rhythm almost always incorporatesmelody or timbre—hence Nzewi’s introduction of the concept of melo-rhythm as a central category into the analysis of African music.37 Definitionally,in other words, rhythm is always already yoked to at least one other dimen-sion. The parallelism of procedure enshrined in the notion of an isomorphismmay well be consistent with the across-the-dimensions thinking enshrined in African vocabularies. If isomorphisms between pitch and rhythm reflect a pres-ent reality, it may be—and this is no more than a wild speculation—that the

36. Benjamin Boretz, “In Quest of the Rhythmic Genius,” Perspectives of New Music 9, no. 2,and 10, no. 1 (Spring 1971): 150. The genius in question is not an African master drummer but a

cosmopolitan Russian by the name of Igor Stravinsky.

37. Meki Nzewi, “Melo-Rhythmic Essence and Hot Rhythm in Nigerian Folk Music,” The Black Perspective in Music 2 (1974): 23–28.




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two dimensions existed together in a distant past. And it may be that current African practice retains vestiges of that past.

Meter and Dance

Like all other time lines, the standard pattern emerges primarily in the contextof dance music, not contemplative, danceless music. While this circumstanceseems obvious enough, it continues to be ignored by the majority of analystsof African rhythm, especially those who encounter African music on audiorecordings and who do not seek out the choreographic element sedimented inthe sounding parts. Yet, without some sense of how individual African com-

munities domesticate the standard pattern in dance, it is not possible to arriveat a correct, culturally sanctioned understanding. This is not necessarily a pleafor the use of dance notation (already undertaken by Hewitt Pantaleoni,Locke, and others, but with limited influence38); it is only an appeal to analyststo draw insight from a competent dancer’s modes of expressing sound inmovement.39

The role of dance in fostering rhythmic understanding is not a uniquely African problematic. Think how greatly our understanding of the eighteenth-century minuet is enhanced by practical knowledge gained from dancing to it.

Understanding form as process, for example, is heightened when one experi-

38. Hewitt Pantaleoni, “Three Principles of Timing in Anlo Dance Drumming,” African Music 5, no. 2 (1972): 50–63; David Locke, “The Music of Atsiagbeko” (PhD diss., WesleyanUniversity, 1978).

39. African communal dances are far too numerous to cite in a single footnote, but readers

who require a point of reference might consult the three-volume JVC/Smithsonian Folkways

Video Anthology of Music and Dance of Africa (VTMV-218E, VTMV-219E, VTMV-220E; dis-

tributed by Multicultural Media, 1996) for excerpts from dances originating in Egypt, Uganda,

Senegal, The Gambia, Liberia, Ghana, Nigeria, Kenya, Malawi, Botswana, and South Africa. Notall excerpts are designed to portray the dance, but a number provide vivid illustration of beat

awareness as expressed in foot (and body) movement. In clip 2-3, for example, children’s gamesfrom Liberia feature an intermittent externalization of the regulative beat. The basic movement of

the hunters’ dance in 2-4 reinforces the beat, but there are occasional departures as dancers re-spond to the narrative obligations of the dance. In clips 2-14 and 2-15B, participants may be seen

stepping directly on the beat. A particularly vivid example is the Ostrich Mating Dance-Game

from Botswana excerpted in 3-8. The basic clap pattern is a 12/8 time line based on the

archetype but expressed as . Men and boys alternate between stepping on the

dotted-quarter beats (as they await their turn) and passing a lifted leg over a bent body (as they

simulate the mating act). Especially pertinent to the discussion in this article are the excerpts

from Ghanaian dances featuring prominent time lines: Adowa (2-17); Agbadza (2-19); Bobobo(2-20); Gome (2-21) and Bawaa (2-28). It should perhaps be emphasized that orientation to the

beat rather than slavish enactment of it is the point at issue. Ojo Rasaki Bakare and Minette Mans

set out some of the interpretive issues raised by African dance in “Dance Philosophies and Vocabularies,” in Musical Arts in Africa: Theory, Practice and Education , ed. Anri Herbst, MekiNzewi, and Kofi Agawu, 215–35 (Pretoria: University of South Africa Press, 2003).




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ences a reprise not as large-scale repetition—as scorism prescribes—but asphysical movement of bodies back to a point of departure, in effect, retracinga known, previously traversed space. (This is not the only way to dance a min-

uet, of course; Z and S formations would deliver a more linear view of form.)Similarly, the rhythmic essence of African dance drumming is conveyed in thedancing that expresses sound in movement, dancing that embodies therhythm’s conditions of possibility. As Nketia puts it, “It is generally the rhyth-mic structure that influences the pattern of [a dancer’s] movement. He de-rives his motor feeling from this rhythmic structure, whose elements hearticulates in his basic movements.”40 In rendering sound as physical action,the dancer captures the essence of a rhythmic texture.

Dance and meter are thus closely related. Dancers are often guided by an

emergent beat that embodies, reflects, or points to the metrical configuration.In general, feet rather than hands, head, or buttocks provide the primary locusof metrical articulation. This is not to say that a dancer literally steps on each of the beats of a given measure—although some dances or moments withinthem feature precisely such direct metrical interpretation—but that the dancerconveys an essential component of the meter in foot movement. The functionof the feet is not merely to mark the beat, however. Patterns of foot (andbody) movement operating temporally within a spatial dimension acquire ad-ditional modes of articulation. Moving a foot, hand, or head through space

engenders a more complex profile than the movements and gestures em-ployed by drummers as they beat their instruments. In drumming, movementis a means to an end, the end being the delivery of a rhythmically mediatedmessage. For the dancer, on the other hand, rhythm guides the production of gesture; the gesture, together with the meanings it makes possible, is an end,not a means. And since dance as a form of social intercourse entertains otherobligations, the normative enactment of the music’s main beats cannot be thedancer’s only responsibility.

To restore the dance to drumming and thence to rhythmic analysis would

deliver a perspective that might cause us to question certain rhythmic proper-ties whose reality we have long taken for granted. The most basic of these isthe almost universal reckoning of the ensemble rhythm of characteristic West African genres in 12/8 meter. Although it might seem almost sacrilegious toquestion its validity, such a critique may well point to ways in which scholarshave privileged representational convenience over conceptual accuracy.

In Southern Ewe dances, the feeling of a beat occurs at or near the dotted-quarter level, not the eighth-note level. Although moments of intensity inperformance may be marked by animated movement, no dancer thinks in

cycles of 12 when interpreting the standard pattern. The evidence of the rateat which the dance feet move is that 4, not 12, is the reckoning that most

40. Nketia, The Music of Africa , 210.




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closely approximates the regulative beat.41 This underlying beat feeling wouldprompt us to rewrite the standard pattern as shown in Example 5, replacingthe earlier additive conception with a divisive one. For if it is normally felt with

a regular dotted quarter beat in attendance (as shown in the lower line ofEx. 5), then the pattern is meaningless without this ecological support. Thisparticular representation should not lead one to infer that the four dotted-quarter beats are articulated by any individual instrument within the ensemble—this may or may not be the case, depending on the dance in question; whatcan be said for sure is that the cycle of four beats is felt and thus relied upon.This is cultural knowledge that players and especially dancers possess; withoutsuch knowledge, it is dif ficult to perform accurately.

If dancers do not dance in 12, why have scholars adopted 12/8 as the mostfelicitous meter for representing the dance? One explanation may be defini-tional: being a compound meter, 12/8 implies an underlying four-beatstructure. 12/8 thus represents a cycle of 4, not a cycle of 12. But if 12/8 rep-resents a cycle of 4, then why not use 4/4? The reason is that subdivisions of the dotted quarter abound such that a rendition in 4/4 would include numer-ous triplet markings; this, presumably, would give the transcription a clumsy look. 12/8 naturally acknowledges the subdivision and therefore dispenses

41. Nketia’s discussion of the regulative beat links it to physical movement: “The regulativebeat may be described as a ‘motor’ beat in the sense that it may be articulated in bodily movement

—in the lurching of the shoulders, wagging of the toes, shaking of the head, stamping of the footand so forth” ( African Music in Ghana , 78). See also the discussion in Gerhard Kubik, “TheEmics of African Musical Rhythm,” in Cross Rhythms 2, edited by Daniel Avorgbedor and Kwesi Yankah, 26–66 (Bloomington, IN: Trickster Press, 1985). Of special interest is Vijay S. Iyer,“Microstructures of Feel, Macrostructures of Sound: Embodied Cognition in West African and African-American Musics” (PhD diss., University of California, Berkeley, 1998).

-.4-.4

Ł Ł ý

Ł Ł Ł ýŁ Ł Ł

Ł ýŁ Ł

Ł ýŁ

Example 5 Standard pattern metrically interpreted

Example 6 Equivalence between 12/8 and 4/4 versions of the standard pattern

-.400

Ł Ł

Ł

Ł Ł Ł Ł Ł Ł Ł Ł

Ł Ł Ł

Ł Ł

Ł

Ł 3 3 33




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with 4/4’s triplet markings. So, although the acoustic traces resulting fromrendering the standard pattern as 4/4 and 12/8 are absolutely identical (thisis shown in Ex. 6), scholars have preferred 12/8 for reasons of convenience—ease of reading.42

Meters signify different things depending on the stylistic conventions gov-erning their use by composers and their interpretation by performers. Since African cultures are primary oral cultures, there are no conventions of metrical writing to be invoked. Representational conventions therefore arise from thecommon practice of scholars. What a given meter means to an individualscholar is not always clear, however. It would seem that Western usage is often—and generally by default—a reference point for African usages. And yet it isnot clear, for example, that 4/4 might signify march or gavotte, 12/8 the pas-

toral, or 3/4 the waltz. Although supportable in some contexts, these associa-tions, even within a relatively stable common-practice period, are somewhatfragile; as such, it would be deeply problematic to apply them to a complexand diverse African context. It would seem that the only certainty about theuse of meter in transcriptions of African music is as a grouping mechanism; nostable qualitative, psychological, or cultural associations are enshrined in me-ter. This explains attempts to erase the normative internal accentual schemesof individual meters by arguing, for example, that beat 1 in 4/4 does not nec-essarily bear the superior accent, or that the four dotted-quarter beats in 12/8

are not differentially weighted, that they are accentless. Meter in this under-standing is little more than a grouping mechanism; it is emptied of all conven-tional association.43

The appropriateness of 12/8 is further undermined by one aspect of its his-tory. In earlier studies by Jones, Pantaleoni, and James Koetting, attempts torepresent the metrical structure of African dance music often laid greatstore by a fastest-moving pulse or elementary pulse, the so-called density referent famously described by Koetting.44 Ignoring the dance feet,Koetting reckoned that, given the fast pace at which rhythmic events

42. Toussaint mentions the isomorphism between 12/8 and 4/4; Nzewi’s brief inventory of time lines acknowledges the equivalence ( African Music: Theoretical Content , 36), as does the

more comprehensive inventory supplied by Bertram Lehmann in his excellent study, “The Syntaxof ‘Clav é.’ ” Readers who are secure in their understanding of 12/8 as a four-beat cycle may wellobject to the present discussion. Yet the twelve-ness of 12/8, the feeling that the eighth note is

the primary referential value, appears as a permanent temptation for a number of writers on

African music, especially those who use the Time Unit Box System (see, for example, James T.

Koetting, “ Analysis and Notation of West African Drum Ensemble Music,” Selected Reports in Ethnomusicology 1, no. 3 (1970): 115–46; and Stone, Music in West Africa ). In other words theapparent four-ness of 12/8 is not as secure in reference to African music as it perhaps is in refer-ence to other traditions.

43. David Temperley sheds much light on the analysis of meter and grouping in African

music generally, and on the standard pattern specifically. See his “Meter and Grouping in AfricanMusic.” See also Justin London, Hearing in Time: Psychological Aspects of Musical Meter.

44. Koetting, “ Analysis and Notation.”




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unfold in Ewe and Ashanti dance-drumming, and given the density ofmicro-articulation, something close to an eighth-note pulse would serve asthe structural reference. But this curious concept of a density referent has

never been a reliable guide to metric understanding anywhere in the world. Suppose, for example, that you are listening to the melody of theopening bars of Beethoven’s Piano Sonata, Op. 2, no. 3, for the first time(Ex. 7). You are asked to notate it. Instead of the clear feeling of four (orperhaps two), you look for the smallest note value to guide your transcription. You proceed to count out the passage in sixteenth notes! The first half note would therefore sound like eight sixteenth notes tied together (as shown inthe example)—an obviously absurd conceptualization to anyone who under-stands the beat structure of the passage.

Yet the reasoning implied here is not so far removed from that which insistson the eighth-note pulse in African music, the eighth note being the shortestof the three most active durations—dotted quarter, quarter, and eighth. Itmight be argued that the busy nature of the textures in West African music—the fact that something literally happens on each eighth note—is adequately conveyed by 12/8 meter. But if the aim is to convey such busyness, then onemight imagine J. S. Bach rewriting the first of his two-part inventions as16/16 in order to indicate the predominance of sixteenth notes. We know,however, that the sixteenth-note level marks a subdivision; it is not the pri-mary beat division. In short, if it indicates a cycle of 12, then 12/8 is morecorrectly understood as a subdivision of the beat; if, however, it is understoodas quadruple meter, then it conveys the beat division. Attention to these dif-

Š

Ý

ÐÐ

ð ð \ Ł Ł Ł Ł Ł Ł Ł Ł Ł Ł l Ł Ł l

Ł Ł

Ł Ł

l

l

Ł Ł

Ł Ł

l

l

½

½

!

Allegro con brio

Example 7 Beethoven, Piano Sonata in C Major, Op. 2, no. 3, first movement

(a) Mm. 1–2

(b) Mm. 1–2, rhythm of melody only, with sixteenth-note “density referent”

ð Ł Ł Ł Ł Ł Ł Ł Ł

Ł Ł Ł Ł Ł Ł Ł Ł Ł Ł Ł

Ł Ł Ł

Ł Ł Ł Ł Ł

Ł Ł Ł Ł Ł

½½




24/47


ferent levels of metrical depth should help transcribers in rendering Africanmusical realities more accurately.45

An enduring obstacle to developing a reliable set of preference rules to fa-

cilitate the assignation of meter to West African dance music stems from thefact that meter is not a statistical or material measure reflecting the confluenceof sounding parts. While a given metrical cycle may be reinforced statistically or phenomenally by an accretion of parts, it may also employ silence as markerof the regulative beat. Rhythmic groups do not necessarily reinforce the rulingmeter. A group may traverse a metric boundary and do so persistently, or giveprominence to an ostensibly weak beat or offbeat. Indeed, as both Kolinskiand Arom have argued, contrametrical organization (where accents conflict with the metric pulsation) predominates over commetrical organization

(where accents coincide with the metric pulsation) in African music, but thisdoes not violate the integrity of the basic metrical cycle.46 Although not every African dance displays these tendencies in equal measure, it is fair to say that inthe case of a standard-pattern territory like the Southern Ewe— which, inci-dentally, is also the site of the most influential theorizing about Africanrhythm—the refusal to assign material weight to the regulative beat in perfor-mance (by employing long, high, stressed, timbrally differentiated, or other- wise marked notes) indexes an aesthetic-structural preference.

The most reliable way to determine meter, then, is to be guided by the feel-

ing of beat expressed in the dancer’s feet.47 (Competent amateurs are morelikely to convey dance beats directly, whereas seasoned professionals may sometimes take those beats for granted.) Within the larger polyrhythmic en-semble, the beat is often closest to the beat level expressed in hand claps andtherefore to the tactus level that the majority of participants feel. Meter hasto be postulated on the basis of these larger considerations; it cannot (always)be inferred from the sounding forms alone. One brings a metric attitude—perhaps even a metric prejudice—to the performance.48

For those who understand analysis as an examination of the internal prop-

erties of a work, the idea that something as basic as meter depends on factorsthat lie “outside” the work may seem troubling. But there is nothing unusualabout this way of proceeding. All listeners bring any number of predispositionsto the act of listening. Listeners of tonal music, for example, rely fundamentally

45. For a clear description of the nature of metrical levels see Fred Lerdahl and Ray

Jackendoff, A Generative Theory of Tonal Music (Cambridge, MA: M.I.T. Press, 1983).

46. Mieczyslaw Kolinski, “ A Cross-Cultural Approach to Metro-Rhythmic Patterns,” Ethno- musicology 17 (1973): 494–506; and Arom, African Polyphony and Polyrhythm , 208.

47. Kubik refers to “a regulative beat, often externalized in the form of dance steps” andnotes that “the Beat accepted by the listeners can be found quite easily by looking at the dancers”(“The Emics of African Musical Rhythm,” 38, 35).

48. Martin Scherzinger clarifies this distinction without necessarily endorsing the viewpoint.See his “Notes on a Postcolonial Musicology: Kofi Agawu and the Critique of CulturalDifference,” Current Musicology 75 (2003): 223–50.




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on certain internalized or naturalized conventions in order to interpret onemoment as tense, another as resolving, one as a beginning, another as an end,one as dancelike, another as proselike. Not all of these are immanent proper-

ties of the individual works; some are perspectives formed from certain ways of world-making. Without this kind of cultural knowledge (often simply takenfor granted), one’s interpretation is likely to be impoverished.

Uninterpreted versus Interpreted Chains

As a further illustration of the metrical attitudes that listeners bring to acts of interpretation, Example 8 lists six time lines in two different notations. On the

left is an uninterpreted series of onsets and durations. In practice, each com-plete series is of course repeated as an ostinato. On the right is the metrical in-terpretation as expressed in various forms of cultural behavior, notably thedance. Each series is now re-notated and rendered as a metrical cycle, com-plete with a time signature to convey grouping and a normative accentualscheme. The uninterpreted chain depicts what any listener hears; the inter-preted chain shows what an acculturated listener understands. How do we getfrom the uninterpreted to the interpreted? We will turn in a moment to theHighlife time line in order to explore one such mode of appropriation. For

now, we might simply note certain kinds of preference. Only in one case doesthe longest duration occur on the downbeat. Onsets are often suppressed,thus giving prominence to offbeats, backbeats, and afterbeats. Patterns fre-quently straddle bar lines. Some include a “disruptive” element that endowsthe pattern as a whole with a dynamic feel; often, such dynamism takes theform of a postponement of closure. These are emphatically not (yet) rules be-cause the sample of six is far too small to support any large claims about African rhythmic practice. They are informal observations that speak to struc-tural choices made within a specific cultural milieu. While they may well reflectdeeper expressive impulses, they may also represent historically arbitrary choices that have hardened into convention. In any case, the point of juxta-posing the uninterpreted with the interpreted is to display the “ what” of met-rical choice rather than speculate on “ why.”

Metric Tendency in the Highlife Time Line

The need to postulate rather then infer meter may be illustrated further by ex-

amining another time line, this one associated with the popular-music genreHighlife.49 If we represent its sounding elements as a sequence of durations

49. On the history of the genre, see John E. Collins, Highlife Time (Accra, Ghana:

Anansesem Publications, 1994).




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and rests—if, in other words, we present it as an uninterpreted or minimally interpreted chain— we obtain the pattern shown in Example 9. A bell, clapper,castanet, or some other instrument beats this pattern repeatedly in the course

of a dance performance. How do cultural insiders assign metrical meaning toit?

To answer this question productively, we might contrast an abstract, theo-retical consideration of possibilities based on well-formedness with a culturally inflected consideration of possibilities based on preference. The pattern’ssounding elements are simple enough: three attack points interspersed withrests, the whole suggesting a cycle of four quarter notes. We might thus assigna 4/4 meter. But meter is more than grouping; it encompasses the internalarrangement of rhythmic elements. How are the elements arranged in the

minds of dancers and informed listeners? If, for the sake of consistency andthoroughness, we dispose the Highlife pattern beginning on successive eighthnotes—if, in effect, we rotate the elements of the pattern— we obtain the re-sults shown in Example 10. There are eight distinct forms. Each is well formedin 4/4, although some would seem better formed than others. Rotations

Ł ý Ł ý Ł Ł Ł 00 Ł ý Ł Ł Ł Ł Ł Ł Ł ý Ł Ł Ł Ł ¼ -.4 Ł Ł Ł Ł Ł Ł Ł Ł Ł Ł Ł Ł Ł Ł

Ł Ł

Ł

Ł Ł

.0 Ł Ł Ł Ł Ł Ł

Ł ý Ł ý Ł Ł Ł 00 Ł ý Ł Ł Ł Ł Ł Ł Ł

Ł Ł ý Ł ý .0 Ł Ł ý Ł Ł Ł Ł ý Ł Ł

Ł ¹ Ł ¹ Ł ¹ ¼ ý 00 ¼ ¹ Ł ¹ Ł ¹ Ł

Uninterpreted

=

Interpreted

=

=

=

=

=

1

2

3

4

5

6

Example 8 Six time lines as uninterpreted and interpreted chains




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0, 2, 4, and (to a lesser extent) 6 as a group seem more felicitous in 4/4 thanrotations 1, 3, 5, and 7. Rotation 0’s one-two-three-rest pattern might invokea march, rotation 2 also begins on a downbeat but incorporates syncopation,rotation 4 gives the “march” a longer starting note, and rotation 6 suppressesthe downbeat of the march but retains a steady succession of onbeats there-after. By contrast, and from an equally “ Western” perspective, rotations 1, 3,5, and 7 appear less conventional because, like rotation 6, they each begin not

with sound but with silence, thereby suppressing their downbeats. Unlike ro-tation 6, however, whose subsequent articulations are onbeats, those of rota-tions 1, 3, 5, and 7 are offbeats. The exceptional form is rotation 5, whichdelays an onset by as much as a beat and a half. This, incidentally, is the maxi-mum delay possible within this particular durational economy of eighths andquarter notes.

The African conception of this time line (as conveyed by dancers) is the ap-parently exceptional version shown as rotation 5 in Example 10. We might ex-plain the pattern by saying that if the normative sequence of 4/4 expressed in

eighth notes is rendered mnemonically as one-and-two-and-three-and-four-and, then the Highlife time line articulates only the last three and s and rendersall the other beats as silences. The dance feet meanwhile mark a 4/4 time asthe regulating framework.

For many Western listeners, perhaps, this particular domestication of thepattern features an unexpected accentuation. And that is because habits of metrical understandi

agawu - 2006 - structural analysis or cultural analysis competing perspectives on the “standard...

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